Pre-Algebra Examples

$\frac{7 v^{4} + 9 v^{3}}{- v^{2}}$

Step 1

Factor $v^{3}$ out of $7 v^{4} + 9 v^{3}$ .

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Step 1.1

Factor $v^{3}$ out of $7 v^{4}$ .

$\frac{v^{3} (7 v) + 9 v^{3}}{- v^{2}}$

Step 1.2

Factor $v^{3}$ out of $9 v^{3}$ .

$\frac{v^{3} (7 v) + v^{3} \cdot 9}{- v^{2}}$

Step 1.3

Factor $v^{3}$ out of $v^{3} (7 v) + v^{3} \cdot 9$ .

$\frac{v^{3} (7 v + 9)}{- v^{2}}$

Step 2

Cancel the common factor of $v^{3}$ and $v^{2}$ .

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Step 2.1

Factor $v^{2}$ out of $v^{3} (7 v + 9)$ .

$\frac{v^{2} (v (7 v + 9))}{- v^{2}}$

Step 2.2

Move the negative one from the denominator of $\frac{v (7 v + 9)}{- 1}$ .

$- 1 \cdot (v (7 v + 9))$

Step 3

Rewrite $- 1 \cdot (v (7 v + 9))$ as $- (v (7 v + 9))$ .

$- (v (7 v + 9))$

Step 4

Apply the distributive property.

$- (v (7 v) + v \cdot 9)$

Step 5

Rewrite using the commutative property of multiplication.

$- (7 v \cdot v + v \cdot 9)$

Step 6

Move $9$ to the left of $v$ .

$- (7 v \cdot v + 9 \cdot v)$

Step 7

Multiply $v$ by $v$ by adding the exponents.

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Step 7.1

Move $v$ .

$- (7 (v \cdot v) + 9 \cdot v)$

Step 7.2

Multiply $v$ by $v$ .

$- (7 v^{2} + 9 \cdot v)$

$- (7 v^{2} + 9 v)$

Step 8

Apply the distributive property.

$- (7 v^{2}) - (9 v)$

Step 9

Multiply $7$ by $- 1$ .

$- 7 v^{2} - (9 v)$

Step 10

Multiply $9$ by $- 1$ .

$- 7 v^{2} - 9 v$